It took at least three business days before I received a response, so I ended up using someone that was recommended to me by one of my current physicians. I think that one should be able to expect a quicker response to an appointment request than that. (I can't remember the exact date I requested the appointment, so I put in the 1st of July. It was a while ago.)
I was looking for an internist and sent a request for an appointment through their website.
She had to look at my thyroid. One of her staff member was abrupt but the doctor herself was great. She listened fully. She asked important questions and prescribed further diagnostic treatment. When the results from the diagnosis came back her staff contacted me immediately with the results.
My doctor Dr. Nigel Walters referred me to her.